已知Sn,Tn,且Sn Tn=7n-3 n 1,求a5 b5
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S15=(a1+a15)*15/2T15=(b1+b15)*15/2所以S15/T15=(a1+a15)/(b1+b15)等差数列,则a8和b8是a1,a15以及b1,b15的等差中项所以a1+a15
S9/T9=9a5/9b5=a5/b5=63/12=21/4S8/T8=4(a4+a5)/[4(b4+b5)]=(a4+a5)/(b4+b5)=56/11S7/T7=7a4/7b4=a4/b4=49/
因为但看1+2+3...+n这个数列,通项公式为n(n+1)/2=n^/2+n/2所以1=1/2(1^+1)1+2=1/2(2^+2)1+2+3=1/2(3^+3)以此类推,提出共因数1/2,合并括号
1.S2n+1=(A1+A2n+1)*(2n+1)/2=(2n+1)*An(由等差中项推导出来),同理T2n+1=(2n+1)*Bn.所以An/Bn=S2n+1/T2n+1=(4n+4)/(2n+3)
Sn=n(A1+An)/2Tn=n(B1+Bn)/2Sn/Tn=(A1+An)/(B1+Bn)然后n代2n-1A2n-1+A1=2AnBn同理S2n-1/T2n-1=An/Bn=7(2n-1)/(2n
∵anbn=2an2bn=a1+a2n−1b1+b2n−1=(2n−1)(a1+a2n−1) 2(2n−1)(b1+b2n−1) 2=s2n−1T2n−1∴anbn=2(2n−1)
由等差数列的性质Sn=na1+n(n-1)d/2=dn2/2+(a1-d/2)n=An2+Bn即A=d/2B=a1-d/2同样地Tn=nb1+n(n-1)p/2=pn2/2+(b1-p/2)n=Cn2
{an}是等差数列,a2=a1+da3=a1+2d....an=a1+(n-1)da(2n-1)=a1+(2n-2)da1+a(2n-1)=2a1+(2n-2)d2an=2a1+2(n-1)d=2a1
4/3S21=(a1+a21)*21/2a1+a21=a1+a1+20d=2(a1+10d)=2a11所以S21=2a11*21/2=21*a11同理T21=21*b11所以a11/b11=S21/T
设等差数列{an}和{bn}的公差分别为d1 和d2,则由题意可得S1T1=a1b1=2×13×1+1=12,即2a1=b1.再由S2T2=a1+a2b1+b2=2a1+d12b1+d2=2
因为等差数列前n项和为Sn=na1+n(n-1)d/2=d/2*n^2+(a1-d/2)*n所以可知等差数列前n项和是关于n的二次函数,且不含常数项.因为Sn/Tn=(7n+45)/(n+3),所以可
等我算算啊,几分钟
S(2n-1)=(2n-1)an,T(2n-1)=(2n-1)an,所以an/bn=S(2n-1)/T(2n-1),所以a9/b9=S17/T17=18/31.
∵等差数列{an}、{bn},∴an=a1+a2n−12,bn=b1+b2n−12,∴anbn=nannbn=n(a1+a2n−1)2n(b1+b2n−1)2=S2n−1T2n−1,又SnTn=7n+
T(n+1)-Tn=a(n+1)=1-a(n+1)-1+an,即a(n+1)=an/2.T1=1-a1,得a1=1/2.∴an是首项为1/2公比为1/2的等比数列,得an=(1/2)ⁿ,同
∵SnTn=n2n+1,∴a7b7=2a72b7=132(a1+a13)132(b1+b13)=S13T13=132×13+1=1327,故选:C.
∵等差数列{an}和{bn}的前n项和分别为Sn和Tn,且SnTn=5n+32n+7,a5b5=9a59b5=s9T9=4825故选B.
S21=(a1+a21)*21/2a1+a21=a1+a1+20d=2(a1+10d)=2a11所以S21=2a11*21/2=21*a11同理T21=21*b11所以a11/b11=S21/T21=
S9=(a1+a9)/2*9=(2a5)/2*9=9a5同理T9=9b5a5/b5=S9:T9=21/4
∵{an},{bn}是两个等差数列∴a1+a15=2a8b1+b15=2b8∴a8/b8=(15(a1+a15)/2)/(15(b1+b15)/2)=S15/T15∵Sn/Tn=(7n+2)/(n+3